246 
MR. J. LARMOR ON A OYNAiVirCAL THEORY OF 
displacement u of the mther and the coordinates u, 6 ^, ... . d,, of the small 
disturbance of the molecule, say terms [c^u + + •••• + c,A) u. In the 
equation of propagation, formed in the Lagrangian manner, p cl-ujdt' will now be 
replaced by ddjdtd (pu + CqU + Cydi + C. 26.2 + ....+ ; while in the equation of 
vibration of the molecule terms of type ddujdd' will occur. The square of the 
index of refraction is thus given by = I {cqU + + Cgdg + .... + c,fi,)ipu ; 
and this leads by analysis similar to the above to a dispersion formula 
/Tj = A + S U\I{V\ 'P')d^ It is to be noticed that, on a mechanical theory, the 
index does not finally tend to unity as the frequency p/27r rises, for when the waves 
have ceased to excite internal vibrations in the molecules the mther is still loaded by 
their inertia ; an exception occurs when the attachment of the molecule to the 
rether is such that, when owing to the high period it is not internally vibrating, the 
rether does not sensibly displace its centre of mass, in Avhich case the constant A is 
unity and there is no effective load on the aether. If we suppose that each molecule 
has an attachment to a very large mass, so as to be practically anchored to it in 
space, this will require us to take one of the natural frequencies to be infinite in the 
above analysis, so that say is zero. When both these characteristics are present, 
we arrive at Lord Kelvin’s formula.t If on the other hand we take the medium to 
be like an elastic jelly, permeated by spherical portions of different inertia and 
elasticity, the problem is a quite different one, which forms in fact a rude mechanical 
analogue of the electric theory; and it was in this way that L. Lorenz indepen¬ 
dently arrived at the specific refraction formula above discussed. 
* An equation equivalent to tliis with <73 • • • • all positive, appears in Selljieier’s original paper 
(‘ Wied. Ann.,’ 1872), based however on a much more special hypothesis. 
t Baltimore Lectures, 1884 ; cf. also present memoir Part I., ‘Phil. Trans.,’ A, 1894, p. 820. In these 
lectures Lord Kelvin, with a view to explaining true absorption without introducing frictional forces 
into ultimate theory, contemplates the molecules as able to take up a vast amount of energy, near 
certain periods, before they attain to a steady state of synchronous vibration ; as however that state 
must come after at any rate some millions of vibrations, and absorption would then cease, it is 
presumably part of the theory that the absorbed energy is constantly being degraded in the molecule 
by a process analogous to fluorescence, and so being got rid of by radiation at a lower period,—or it 
may be simply scattered owing to change of orientation of the steady state of vibration at which the 
molecule has arrived, due to encounters with other molecules, as indicated by Janssen's law (supra) for 
gases. In the electric theory, metallic absorption is here taken to be chiefly due to the presence of 
free ions or electrons ; but in weakly absorbing media it is probable that the former cause is the 
effective one. The only analytical way open for representing it is to introduce an absorption coefficient 
expressing the averaged rate at which the energy of the radiation is being exhausted. 
The synchronously vibrating material molecules would not in any case give rise to further absorption 
by sending out energy in regular secondary waves ; their uniformity in distribution and phase prevent 
this, just as they prevent the separate elements of the continuous lether from acting in the same way. 
The dust particles which give rise to the blue sky are irregularly distributed, and the individual 
secondary waves thence originating have irregular and independent phase-diffei’ences with reference to 
